Earnings Announcement Clustering, Systematic Liquidity Shocks, and Expected Returns
Paul Brockman* College of Business 513 Cornell Hall University of Missouri Columbia, MO 65211-2600 Tel: (573) 884-1562 Email: [email protected]
Andrei Nikiforov College of Business 508 Cornell Hall University of Missouri Columbia, MO 65211-2600 Tel: (573) 884-7868 Email: [email protected]
Acknowledgements: We would like to thank Sterling Yan, Stephen Ferris, John Howe, Douglas Miller and seminar participants at the University of Missouri for their valuable comments.
Earnings Announcement Clustering, Systematic Liquidity Shocks, and Expected Returns
Abstract Previous studies show that systematic liquidity shocks generate liquidity risk premia that are priced in capital markets. Recent research finds that liquidity betas and risk premia are time-varying. In this study, we hypothesize and confirm that earnings announcement clustering is a significant source of time variation in liquidity betas and liquidity risk premia. First, we document strong market-wide liquidity patterns induced by announcement clustering during the earnings season. While earlier studies analyze liquidity patterns around individual firm announcements, we examine market-wide patterns caused by calendar-time clustering. Second, we show that the sensitivity of stock returns to changes in market-wide illiquidity (i.e., liquidity betas) increases significantly during the earnings season. Third, we show that the impact of time-varying liquidity betas on liquidity risk premia is statistically and economically significant. Earnings announcement clustering is responsible for incremental liquidity risk premia in the range of 0.50% to 2.40% per year. Key Words: Earnings season, clustering, liquidity, risk premium JEL: G12, G14
1. Introduction In this study, we argue that earnings announcement clustering during earnings seasons can have significant effects on stock market liquidity, liquidity betas, and liquidity risk premia. Since the information flow is highly concentrated during a very short interval, this creates a potential for market-wide liquidity shocks. These shocks result in time-varying liquidity risk which in turn leads to changes in the liquidity risk premium that investors require to hold the stocks. We estimate that the marginal liquidity risk premium lies in the range between 0.5% and 2.4% per year. Earnings season is arguably one of the most important time periods on Wall Street. During these periods very important economic information floods the market keeping busy thousands of analysts, professional and amateur traders, and the business press. In spite of its significance for the Wall Street and practitioners in general, this unique period of the year has received scant (if any) attention from academia. This is surprising since as soon as one deviates from the world of perfect and complete information, the importance of information arrival (how, when, and how fast) on asset prices becomes significant (see O'Hara (2003) for a general discussion). Even though the clustering effect of earnings seasons has been ignored, there is a vast stream of literature in finance and accounting that studies the impact of individual firm‟s earnings announcements on financial markets. Numerous studies have shown that bid-ask spreads widen and depths on the limit books substantially decrease around individual firms‟ earnings announcements. In addition, trading volumes sharply decrease just before 2
announcements and surge right after the announcements (Chae (2005). Most authors conclude that the observed patterns are best explained by the changing information environment around these events. There are, however, several ways in which the information environment can affect asset prices. When a company announces its quarterly earnings, the opportunity for informed trading (whether by insiders or better information processors) is arguably at its highest. Even though none of the previous studies looks at how the changing information environment impacts asset prices, there are many studies that argue that the proportion of informed to uninformed (noise or liquidity) traders matters enough to affect required rates of return. For example, Easley et al. (2002) develop a multi-asset rational expectations equilibrium model in which stocks have differing levels of public and private information. They show that in equilibrium, uninformed traders require compensation to hold stocks with greater private information, resulting in crosssectional differences in returns. Admati (1985) generalize Grossman and Stiglitz‟s (1980) analysis of partially revealing rational expectations equilibrium to multiple assets and show how individuals face differing risk-return trade-offs when differential information is not fully revealed in equilibrium. Wang (1993) provides an intertemporal asset-pricing model in which traders can invest in a riskless asset and a risky asset. In his model, the presence of traders with superior information induces an adverse selection problem, as uninformed traders demand a premium for the risk of trading with informed traders. The ability of the information environment to affect liquidity is thoroughly documented. The sharp changes in the information environment, and more specifically in adverse selection, directly affect stock liquidity, and if the changes in liquidity across stocks are correlated, asset prices. Kim and Verrecchia (1991) and Frazzini and Lamont (2006) show that the sensitivity of 3
prices to volumes increases substantially around earnings announcements and demonstrate that market makers insure themselves against higher possibilities of informed trading by widening spreads and reducing the number of shares they are willing to buy or sell at any quoted price level (Koski and Michaely (2000)). Given that the earnings announcements by thousands of firms are densely packed into the so-called earnings seasons (40 to 45 day window after the end of each calendar quarter), it is natural to hypothesize that all the small individual liquidity impacts will add up to market-wide liquidity shocks. Combining this observation with the burgeoning literature on the commonality in liquidity (Chordia et al. (2000)) led several authors to conclude that systematic liquidity risk is priced in the cross-section of stock returns (e.g., Pastor and Stambaugh (2003) and Acharya and Pedersen (2005)). We further hypothesize that this commonality could, in part, be caused by the liquidity impacts of the earnings announcement clustering during earnings seasons. In addition, since the earnings seasons come and go turning into relatively “calm” periods, we speculate that the liquidity risk (and not just the liquidity level) also changes across these time periods. Our main hypothesis is closely related to the models proposed by Gallmeyer et al. (2005) who show how sudden changes in heterogeneous investors‟ information sets lead to high and low preference-uncertainty periods. During these periods, investor uncertainty about each other‟s preferences is at its highest. Watanabe and Watanabe (2008) add transaction costs to Gallmeyer et al.‟s (2005) model and demonstrate how these periods (identified by a surge in trading volume) lead to fluctuating liquidity risk. Gallmeyer et al. (2005) hypothesize that the possible sources of preference risk could include endowment shocks (Constantinides and Duffie (1996)), stochastic risk aversion (Campbell et al. (1993) and Gordon and St-Amour (2000)), the size of the pool of investors (Smith (1993)), funding and capital adequacy constraints, and uncertain 4
subjective discount rates. Any (if not all) of the above reasons could play a role during earnings seasons. We posit that earnings seasons are a good candidate for the high-preference-uncertainty periods, especially given their impact on trading volumes and volatility. We argue in this paper that earnings seasons can be viewed as the periods with high preference risk – when investors do not know how other investors will respond to ongoing and future events. We study how liquidity risk changes during earnings seasons using the framework employed in Gallmeyer et al. (2005) and Watanabe and Watanabe (2008). Our findings can be summarized as follows. First, we document strong market-wide liquidity patterns induced by announcement clustering during the earnings season. Second, we show that the sensitivity of stock returns to changes in market-wide illiquidity (i.e., liquidity betas) increases significantly during the earnings season; and third, we show that the impact of time-varying liquidity betas on liquidity risk premia is statistically and economically significant. The paper consists of two main parts. The first part (section 2) establishes the significance of the earnings seasons for the financial markets. We discuss the basic institutional features that define earnings seasons and then briefly review the literature that documents the impact of individual earnings announcements on financial markets. This part sheds light on the clustering effect of earnings seasons through its effects on market-wide returns, volatility, and trading volume. In the second part of the paper (section 3), we investigate the asset pricing implications of liquidity changes caused by earnings announcement clustering. Specifically, we study the changes in liquidity betas and changes in conditional liquidity risk. In the concluding part of the paper (section 4), we summarize the study and make several suggestions for future research.
2. Earning announcement clustering and liquidity effects 2.1. Seasonality in earnings announcements 2.1.1. General background on regulation
According to the Securities Exchange Act of 1934 (the Act) every public company (with float of at least $74M) must report their quarterly and annual results within a certain time period following the end of their fiscal quarters and years. Specifically, the Act states that all public companies must file quarterly reports within 45 days after the end of a fiscal quarter (40 days for companies with market value of $700M or more) and annual reports within 90 days following the end of the company‟s fiscal year (75 days for firms with market value of $700M or more).1 In 2002, the SEC published a new rule in order to accelerate the filing of these documents that reduced the number of days to 35 for quarterly reports and 60 for annual reports.2 2.1.2. Distribution of earnings announcements
We use the COMPUSTAT Industrial Quarterly database which reports the date when the earnings report was made available to the public for the first time (through the publication in the Wall Street Journal or newswire services.) Even though the database coverage starts in December 1970, the coverage is incomplete in the early years of the sample. The coverage of earnings announcement rises from 50% in 1974 to 95% in 2005 (for 2006 the coverage is still incomplete as of December 2007). Figure 1 illustrates the coverage of reporting firms from 1971 to 2006. The figure confirms that the coverage was relatively sparse in the 1970s and 1980s gradually increasing in the 1990s, reaching a peak in 2001. The coverage dropped somewhat in the 2003-2006 period probably due to the merger wave and the bursting of the internet bubble. 1 2
See the Federal Regulation Code Title 17 parts 230 through 250 for terms and definitions. RELEASE NOS. 33-8128; 34-46464; FR-63; (http://www.sec.gov/rules/final/33-8128.htm)
We expect that the legally specified reporting intervals will result in strong seasonality (or clustering) of earnings releases. Although the seasonality is very strong, there are some leakages. The main reason is that roughly two-thirds of all companies have their fiscal year ends in December with the rest filing their annual reports throughout the year. And since the reporting interval for annual reports is 75 to 90 days, there is usually not a single day in a year without a company reporting. Table 1 shows the distribution of announcements and fiscal year-ends by calendar month.3 Most firms (around 60%) have December fiscal year-ends, while others have March (6%), June (8.9%), and September (7%) year ends. For the non-quarter-end months, the percentage of firms‟ reporting is fairly small – typically between 1 and 3 percent. Next, we investigate the actual seasonality in earnings announcement clustering in a typical year to select the most representative time periods as our “earnings seasons.” Figure 2 shows the average number of weekly reports for a period from 1971 to 2006. The seasonal pattern is striking. We can clearly identify the four earnings seasons, three of which are of the same form. We also see that the patterns for January and February are somewhat different from the rest of the year. This corresponds to the fact that for most firms December is the fiscal yea end and so they have 75 to 90 days (instead of usual 30 to 45) to report their earnings. As a result, earnings reports in January are lower than at the end of other quarters. The lowest number of announcements corresponds to the first and last weeks of each quarter. The highest peaks correspond to the third and fourth weeks of each quarter, with slight declines during weeks five and six. A substantial number of firms procrastinate until the last day of the allowed period. The number of firms reporting during the fourth week of the quarter (the highest peak) is on average seven times greater than the number of firms reporting during the first week and the 3
The proportions of firms having fiscal year ends other than December stay fairly constant from 1971 to 2006.
last week (the lowest). The average number of firms reporting during the whole earnings season (the first six weeks of each quarter) is three times the number of firms reporting outside the season. These results show that there is a strong seasonality or clustering in the discharge of economically significant information in the US economy. 2.1.3. Individual earnings announcements
Previous studies have focused on the impact of earnings releases on individual firms‟ price, volatility, volume, liquidity, and adverse selection (Lee (1992) and Lee et al. (1993)). The most pronounced feature of any (scheduled) earnings release is the distinct pattern in the trading volume. The number of shares traded falls sharply below the long-term average and then dramatically surges immediately following the announcement (Chae (2005)). The usual explanation (George et al., (1994) is that uninformed traders understand their informational disadvantage just before the earnings release and wait until after the event, when the uncertainty is partially resolved, to continue their trading. Market makers are aware of the active presence of informed investors and, facing adverse selection, manage this risk by widening bid-ask spreads and decreasing depths (Lee et al. (1993), Krinsky and Lee (1996), and Kavajecz (1999)). The existence of intra-industry information transfers suggests that earnings seasons could have market-wide effects on liquidity. Foster (1981) initiates this stream of research by showing that a single earnings announcement affects not only the reporting firm but also the other companies in the same industry. Kovacs (2005) finds that a firm‟s stock price is positively related to industry peers‟ earnings surprises regardless of whether the firm has already announced its own quarterly earnings. This finding suggests that earnings announcements contain industry-relevant information that is not fully captured by a firm‟s own earnings. Sun (2006) investigates the timing of an announcement within the earnings seasons and finds 8
evidence consistent with information transfers. He reports that late-reported good news announcements are accompanied by significant pre-announcement price increases. In addition, firms provide much more information in their earnings releases than just past the quarter‟s earnings. Brandt et al. (2006) note that firms‟ press releases elaborate on the earnings report as well as provide forward looking information. For example, firms provide expanded information about components of earnings such as sales and operating margin as well as future sales forecasts. Although significant information (i.e., same-store sales, consumer sentiment index, etc.) is released throughout the year, it is difficult to overestimate the importance of earnings releases. Chiang and Mensah (2006) investigate the inferential value of earnings releases by comparing them with other sources of information. They find that excess returns measured around earnings announcements are more highly correlated with changes in future firm performance than similar measures in non-disclosure periods. They conclude that earnings reports provide a more definitive basis for the capital markets to scrutinize previous assumptions than that provided by alternative sources. 2.2. The market-wide effect of earnings announcement clustering
In this section, we document the effects of earnings announcement clustering on marketwide stock returns, trading volume, and volatility. 2.2.1. Returns
The stylized fact that the returns increase during the first two weeks of earnings seasons has long been established. Penman (1987) argues that aggregate returns tend to be positive because firms with very good news tend to release their earnings figures in the first two weeks. He identifies this seasonality in index returns over a period of 20 years (up to 1982). No other 9
study has updated the results but it seems that the results could be driven by the January effect since he does not control for it. We investigate this issue with a much longer time-series spanning from 1962 to 2006. We test for seasonality in returns over three different periods all related to the earnings seasons. The first period is the first two weeks of each earnings seasons, the second is the first month of the earnings seasons (January, April, July, and October), and the third period is the full 45-day window after each calendar quarter when all firms have to report their quarterly numbers. The results in Panel A of Table 2 show that the seasonality is present in equal-weighted but not value-weighted return series. This may be due to smaller firms having greater sensitivity to earnings news. Unlike big firms which are usually followed by analysts and business press, small firms are more likely to have most of their relevant information released during the earnings seasons with little news released at other times. Amihud (2002) argues that if earnings seasons are characterized by higher nondiversifiable information (or preference) risk, then stocks that are most sensitive to this risk should provide investors with higher expected returns. To provide these higher expected returns, we expect that stock prices will decline during earnings seasons. Our findings in Panel A of Table 2 seem to contradict the above analysis. For all three period lengths, realized returns during the earnings seasons are higher than the returns during regular seasons (significantly higher for equal-weighted confirming our conjecture about the effect on small firms). However, Keim (1983) and Reinganum (1983) show that much of the abnormal return to small firms (measured relative to the CAPM) occurs during the first two weeks in January. Roll (1983) hypothesize that the higher volatility of small-capitalization stocks causes more of them 10
to experience substantial short-term capital losses that investors might want to realize for income tax purposes before the end of the year. This selling pressure might reduce prices of small-cap stocks in December, leading to a rebound in early January as investors repurchase these stocks to reestablish their investment positions. To control for this effect, we exclude the first two weeks of January from our analysis. This significantly changes the results, as presented in Table 2 Panel B. The returns change from slightly positive to negative (significantly negative at 5% for equal-weighted market returns). After controlling for the January effect, the overall results corroborate our hypothesis about realized returns during earnings seasons. 2.2.2. Trading volume
Although volume is one of the most important characteristics of a stock market, a comprehensive theory of volume is still not in sight. In a rational expectations (homogeneous agents) framework, information does not cause agents to trade (the “no-trade” theorem – see, for example, Milgrom and Stokey (1982)). Instead, prices just change without any trades. This is completely opposite to what we observe in real stock markets: volume surges with the arrival of new information. Gallmeyer et al. (2005) working with heterogeneous agents hypothesize that the new information causes changes in investors‟ preferences and so volume increases in response to the need to adjust the portfolios to the new market conditions. Since earnings seasons are characterized by the release of new and important information in a very short period of time, we hypothesize that this period of time will be accompanied by significant changes in trading volume. We cannot predict the direction (up or down) since the earnings are characterized by a sharp drop in volume just before the announcement and a surge just after. We can speculate though that as the earnings season starts, trading volume will fall since the probability of informed trading increases rapidly and liquidity/noise traders drop out of the market. 11
One of the difficulties in measuring trading volume is the choice of an appropriate metric. Lo and Wang (2000) analyze most of the measures used to compute volume and grouped them into five commonly used sets. They then perform a “horse race” and conclude that the best measure of trading volume is share turnover (the number of shares traded as a percent of total shares outstanding). However, since the share turnover is very sensitive to transaction costs (lower costs associated with higher turnover) and the transaction costs dropped precipitously during the last 10-20 years, the time series needs to be scaled. We follow a conventional approach and define the share turnover as a ratio of the average number of shares traded during a week to the average number of shares outstanding during that week. To eliminate possible serial correlation and to account for the decreasing transaction costs during the study period we scale the turnover time-series by a 24-week average. The same approach is used in Eckbo and Norli (2002) and Watanabe and Watanabe (2008). A typical annual pattern of trading volume fluctuations is presented in Figure 3. We average weekly trading volumes over 45 years (1962-2006) and impose them on the graph showing the average number of firms reporting during a particular week of the year. As seen in the graph, trading volume exhibits the same well-known pattern detected in several studies (e.g. Statman et al. (2006)) with high values at the beginning and end of the year and very low values in the middle. The second observation is that there is a clear quarterly pattern with high turnover in the middle of a typical earnings season and low turnover at the beginning and end. After running simple OLS regressions with dummies for different weeks of the year (using dummy variables to test the four different period lengths: first two weeks, middle two weeks – the peak of the season, one month, and the full 45 day season), we find that the first two weeks of a new quarter is characterized by a significant decrease in trading volume (see Table 12
3), if we control for the January effect. Testing the next two weeks (the peak of the earnings seasons), we find that volume is significantly higher. The last two rows in Table 3 show that the regressions that use one month and the full season (45 days) produce insignificant coefficients. We also observe that the January effect plays a significant role in driving the average yearly volume up and, therefore, it is important to control for this effect. 2.2.3. Volatility
It is well known that the volatility of stock returns varies over time. This variation can induce changes in the investment opportunity set by either changing the expectation of future market returns or by changing the risk-return trade-off. The main reason for the variation in volatility is economic uncertainty (Schwert (1989)). Veronesi (1999) presents a theoretical model that formalizes the link between economic uncertainty and stock market volatility. He shows that investors are more sensitive to news during periods of high uncertainty, which in turn increases asset price volatility. Since the earnings seasons are characterized by a highly concentrated dissemination of information about companies‟ fundamentals, we hypothesize that these periods will be accompanied by heightened aggregate stock market volatility. To test our conjecture we need to choose a measure of volatility. The difficulty of using volatility as a variable is that this economic factor is not observable. Instead, we have to infer it from the returns data which requires making certain assumptions. Using realized squared returns gives a simple estimate of volatility but it can be unreliable because it assumes normality and a white noise process (which is at odds with seasonal patterns). ARCH/GARCH and stochastic volatility frameworks are more flexible on the one hand, but require a lot more assumptions on the other (Tsay (2005)).
An alternative measure of volatility that has become the measure of choice for academics in the last decade is the CBOE Volatility Index (VIX). Ang et al. (2006) investigate the performance of different volatility measures and found VIX to be the most appealing. VIX provides a minute-by minute snapshot of expected stock market volatility over the next 30 calendar days. This volatility is calculated in real-time from stock index option prices and is continuously disseminated throughout the trading day.4 VIX estimates expected volatility from the prices of stock index options in a wide range of strike prices, not just at-the-money strikes. VIX is independent of any particular model and uses a newly developed formula to derive expected volatility by averaging the weighted prices of out-of-the money puts and calls. After calculating weekly VIX values and computing the innovations in volatility (by finding the first difference)5 we run simple regression models to check for seasonality in the innovations. We find that the only week (of each quarter) where innovations in VIX are significantly higher (p-value = 0.037) is the last week of the quarter; or, equivalently, the week just before earnings seasons. By the definition of VIX, this result means that during the last week of the calendar quarter, the expected volatility over the next 30 days (the larger part the earnings season) is significantly higher than the expected volatility during any other time of the year. 2.2.4. Summary
As we can see from the above analyses, the aggregate effect of the earnings seasons on the financial markets is significant. In particular, realized returns are lower (especially for smaller stocks) when we control for the January effect. Trading volume (share turnover) is significantly lower during the first two weeks of the earnings season and significantly higher
See CBOE website http://www.cboe.com/micro/vix/vixwhite.pdf . VIX is very persistent with serial correlation of more than 90% (Ang et al. (2006)).
during the rest of the season. Lastly, volatility (VIX) reaches its highest point precisely during the week before the start of earnings seasons, suggesting that investors expect the next month to be especially unpredictable. After establishing the economic significance of earnings seasons, we next investigate the impact of earnings announcement clustering on liquidity betas and liquidity risk premia. 3. Liquidity betas and liquidity risk premia 3.1. Overview and hypotheses development
Several studies document the existence of aggregate fluctuations in liquidity and its effect on asset prices. Chordia et al. (2000) introduced the term “commonality in liquidity”. They argue that liquidity, trading costs, and other individual microstructure phenomena have common underlying determinants and that some portion of individual transaction costs co-vary through time. They suggest several sources of commonality in liquidity: variation in dealers‟ inventory levels, variation in market-wide volatility, and program trading. They also pose the question whether variations in asymmetric information could have a market-wide component and therefore be another important source of commonality in liquidity. Huberman and Halka (2001) document the presence of a systematic time-varying component in liquidity by finding seasonal regularities in the bid-ask spread of the NYSE-traded stocks. As soon as commonality in liquidity was well established, several studies looked at how the systematic component of liquidity affects asset prices. Chordia et al. (2001) investigate the relationship between trading activity and expected stock returns. To their surprise, they find that there is a strong negative correlation robust to different model specifications. Pastor and Stambaugh (2003) show that it is not the volatility in the individual stock‟s liquidity per se that is 15
important to investors but rather the sensitivity of this liquidity variation to aggregate market liquidity fluctuations. They find that stocks‟ liquidity betas, the unconditional sensitivities to innovations in aggregate liquidity, play a significant role in asset pricing. The inclusion of the Fama-French risk factors as well as momentum into the model does not eliminate the liquidity effect. Longstaff (2005) and Acharya and Pedersen (2005) develop theoretical models showing how the innovations in aggregate liquidity are priced when trading costs are included in the models. Even though many papers find that the fluctuations in aggregate liquidity have systematic components and should be priced, only a few explanations of such variations have been proposed. These explanations range from compensation for transaction costs to random marketwide shocks to liquidity (such as a country crisis) to somewhat more exotic explanations. For example, DeGennaro et al. (2006) explain the seasonal variation in bid-ask spreads by the socalled Seasonal Affective Disorder (SAD). They argue that the number of daylight hours a day strongly influences the risk-aversion of traders and market makers. One of the main puzzles that emerges from the fact that liquidity is priced is a simple observation that investors can easily avoid (or significantly reduce) their transaction costs by simply reducing their trading (Constantinides (1986)). If investors can avoid this cost, why should it be priced? Several hypotheses were put forward to explain the phenomenon. All of them are based on the assumption that the liquidity cost proxies are highly correlated with other sources of risk that could be priced and, therefore, the observed liquidity risk premium is in fact a premium for these unobservable sources of risk.
Huang (2003) developed one of the first models in this area. He assumes that agents face surprise liquidity shocks and invest in liquid and illiquid riskless assets. The random holding horizon from liquidity shocks makes the return of the illiquid security risky. He finds that illiquidity can have large effects on asset returns when agents face liquidity shocks and borrowing constraints. Easley et al. (2002) and O'Hara (2003) focus on differences in information sets across investors, and find that information-based trading has a large and significantly positive effect on asset returns. Uninformed traders understand that they will lose to better informed agents, but since they still have portfolio choices to make, they choose assets in which information risk relatively low. Gallmeyer et al. (2005) address the problem by assuming that investors are asymmetrically informed about each others‟ preferences and that trading is an important source of revealing this information. This preference uncertainty can expose investors to resale price risk because they are uncertain about the future asset demand of trading counterparties. Trading helps to reveal preferences (fully or partially) so that the level of preference risk is endogenously determined. They also assume the stochastic nature of changes in future preferences, and hypothesize the existence of high and low preference risk environments concluding that the preference risk is priced in equilibrium. Watanabe and Watanabe (2008) extend the model to study the effect of time-varying liquidity risk on the cross-section of stock returns. They introduce liquidity costs into Gallmeyer et al.‟s (2005) model and hypothesize that liquidity betas are positive and larger during the periods when investors face a higher level of preference uncertainty, and that the liquidity risk premium also rises during the times of high preference uncertainty.
What is common across Huang‟s (2003) and Gallmeyer et al.‟s (2005) model is the existence of two time periods with different levels of risk. Huang (2003) needs periods with liquidity shocks and Gallmeyer et al. (2005) postulate periods with high and low preference uncertainty. Even though Easley et al. (2002) assume constant PIN for each firm, they speculate (see footnote 8) on whether there is a common (systematic) time-varying component in private information across stocks. In this paper, we argue that the clustering of earnings announcements during earnings seasons is an ideal candidate for a period of high-level risk (be it high illiquidity, high preference uncertainty, or high probability of informed trading). The recognition and documentation of this fact is the main contribution of this study. Following the framework developed in Gallmeyer et al. (2005) and Watanabe and Watanabe (2008), we first examine the effect of preference uncertainty during the earnings seasons on liquidity betas. We argue that during the earnings seasons the liquidity betas will be larger in magnitude (more negative) than during the regular seasons. The logic of the argument is as follows. Although earnings seasons are well known in advance, the content of the information flow is stochastic which leads to a stochastic change in investors‟ expectations and illiquidity. When there is an unanticipated increase in the next period‟s illiquidity cost, it will also raise subsequent periods‟ costs due to persistence in illiquidity, which is widely documented in the empirical literature (Amihud (2002)). The rise in future illiquidity costs will in turn decrease the next period‟s price, because it is the sum of discounted future payoffs after cost, leading to a larger return decrease under higher preference uncertainty. This process results in a lower current price that marginal investors require in order to compensate themselves for future resale price risk. This same argument is also formally developed in Acharya and Pedersen (2005). 18
Based on the above analysis we expect that the liquidity beta of an asset will be negative in part because a rise in market illiquidity reduces asset values. This beta affects required returns negatively because investors are willing to accept a lower return on an asset with a high return in times of market illiquidity. Consequently, the more negative the exposure of the asset to market illiquidity, the greater the required return (Amihud et al. (2005)). Therefore, our first testable hypothesis is that the return sensitivity to illiquidity shocks is negative and larger in magnitude, or equivalently, liquidity betas are more negative when investors face a higher level of preference uncertainty. Next, the changing level of preference uncertainty during the earnings seasons will also affect the liquidity risk premium. Liquidity risk is priced because illiquidity shocks make investors‟ consumption volatile and risk-averse investors dislike volatile consumption; the more volatile their consumption becomes, the more risk premium they will require. We propose that preference uncertainty during earnings seasons makes their consumption more sensitive to the illiquidity shocks and hence more volatile, because the sensitivity is proportional to trading volume. Intuitively, as investors accommodate larger sell trades from their counterparties under higher preference uncertainty, they will have to pay more illiquidity costs when they close out their positions in the future. This leads to our second hypothesis that the liquidity risk premium rises during the earnings seasons. 3.2. Data and methodology
We begin our empirical analysis by examining the changes in liquidity betas across the two seasons (earnings vs. “calm”). We use two extreme size deciles of size-sorted portfolios given by the value-weighted size-sorted portfolios of stocks listed on the New York Stock 19
Exchange (NYSE), the American Stock Exchange (AMEX), and NASDAQ all obtained from CRSP database for the period from 1962 to 2006. To account for the “double-counting” of volume for the NASDAQ stocks we divide their reported volumes by half (Atkins and Dyl (1997), Anderson and Dyl (2003)). Another potential drawback of including the NASDAQ stock is that the time-series for the majority of stock starts only in the late 1970s and early 1980s and thus the sample size substantially increases after that period. We address both problems in the robustness section of the paper where we run our tests on the smaller sample that excludes NASDAQ firms. Most studies on the asset pricing implications of liquidity use monthly returns. However, as we saw in the previous section earnings seasons‟ information flows peak at the end of week four and remains elevated from week two to week seven. To preserve the monthly time period in this study and to capture the effect of earnings seasons we shift all months two weeks forward. For example, our January month starts on January 16th and ends on February 14th and we did so for each month. To get monthly stock and factor returns we used compounded daily returns from the CRSP daily stock file calculated over our redefined months. Since the earnings seasons can be perfectly identified, we test our first hypothesis using a simple OLS regression with dummy variables for earnings seasons. Specifically, the dummy variable ES is defined as one if the (shifted) months are January, April, July, or October and zero otherwise. Specifically, we fit the following OLS model to the excess returns of the smallest and largest size-decile portfolios: (1)
where INILt is the innovation in the illiquidity factor (described below and called simply the “liquidity factor” thereafter); rt is the series of excess returns on the smallest or the largest decile portfolios; and βINIL is the liquidity beta. If βINIL*ES is positive and significantly different from zero, then the betas during the earnings seasons and the “calm” periods have different slopes. We expect more negative betas during the earnings seasons, ES, which would be consistent with our first hypothesis. The product of variables ESt and INILt equals INIL during the earnings season and zero otherwise. In other words, it is a Liquidity factor conditional on earnings seasons. We denote it as INILESt in our further analysis and instead of writing a somewhat cumbersome βINIL*ES we use βINILES. Equation (1) does not control for factors commonly used in asset pricing tests. We argue that this is sufficient for the unconditional state identification. For example, if we include the market return, the estimated liquidity betas would be those conditional on it (see a similar argument in Watanabe and Watanabe (2008)). Also, we know that unexpected liquidity shocks and the market return are correlated (Amihud (2002)), and we consider the level of the market return (and possibly other variables) to be an important characteristic of earnings seasons. We use full specification models in the asset pricing section of this paper. 3.3. Liquidity measure
Researchers have used several methods to create monthly liquidity factor for asset pricing tests. Hasbrouck (2006) conducts a “horse race” among different measures of liquidity and concludes that „„among the proxies considered here, the illiquidity measure [proposed by Amihud (2002)] appears to be the best.” The same price-impact proxy was used in Acharya and Pedersen 2005 as a measure of illiquidity costs. Following these suggestions, we compute ILLIQ as: 21
where D is the number of trading days in stock j in month t, and r and vol are daily return and trading volume, respectively. Following other studies we use only ordinary common shares (SHRCD equals 10 or 11 in CRSP database) on NYSE , AMEX, and NASDAQ with Dj,t >= 15 and the beginning-of-themonth price between $5 and $1,000. The aggregate price impact (AILLIQt) is simply the cross sectional average of individual ILLIQ over month t from August 1962 to December 2006. Since the illiquidity series is very persistent, we follow Acharya and Pedersen (2005) and use an AR(2) model to extract innovations. Specifically, we fit the following model: (3) where
is the ratio of market cap of the stocks used to calculate AILLIQt at the end of the
previous month to the total market value of the used stocks in August 1962. This ratio is used to control for the decreasing time trend in AILLIQ and makes the time series more or less stationary. Following Acharya and Pederson (2005) we use the estimated residuals, εt as our liquidity measure (innovation in illiquidity), INILt, which starts in October 1962. 3.4. Variation in liquidity betas
The results of the OLS regression with dummy variables are presented in Table 4. Consistent with our first hypothesis we find a significant and negative relation between liquidity shocks during the earnings seasons and contemporaneous returns (that is, returns are higher for more liquid stocks), as indicated by significant and negative liquidity betas (both βINIL and βINILES are negative and significant at the 3% level) for the smallest and the largest decile portfolios. 22
The likelihood ratio test rejects the null hypothesis that the two betas, βINIL and βINILES, are the same at the 1% level. We therefore conclude that the sensitivity of returns during the earnings seasons to liquidity shocks is substantially higher (or more negative) than during non-earnings seasons. This finding stresses the importance of the earnings seasons for market-wide liquidity since it is consistent with other findings in Amihud (2002), Pastor and Stambaugh (2003), Acharya and Pederson (2005) and others who also find that the contemporaneous returns decline with higher illiquidity. A notable additional finding from Table 4 is the cross-sectional difference in liquiditybeta spreads. The spread of the estimated parameters between the two states is 0.00031 (= 0.00407 – (-0.00376)) for the smallest decile and 0.00155 (= -0.00259 – (-0.00104)) for the largest. The most striking fact is that the largest stocks experience greater sensitivity to the fluctuations in market illiquidity during earnings seasons. In fact, since we measure the additional sensitivity, it is only natural to expect that the bigger and most followed stocks will be most affected by the unexpected liquidity shock during the season when both analysts and investors are closely watching the stocks. Despite the fact that the incremental sensitivity is larger for the largest decile, the absolute values of the liquidity betas are more than two times bigger for the smallest stocks. A very similar pattern was observed in Chordia et al. (2000). This result agrees exactly with both Amihud (2002) and Acharya and Pedersen (2005) who show that small illiquid stocks have higher liquidity betas (more negative) than large liquid stocks on average. However, our results add to their findings by documenting new evidence that such crosssectional asymmetry in liquidity betas exhibits state-dependent time variation. The last two columns report the results of the test when all portfolios are used to check if the results are not 23
driven by the extreme stocks. We find that all of the coefficients preserve their significance, signs, and magnitudes. 3.5. Time-varying liquidity risk premium
Following Watanabe and Watanabe (2008), we define the conditional liquidity factor as: INILESt=ESt*INILt
where ESt is an indicator variable that takes a value of 1 during the earnings season (shifted) months and 0 otherwise. To understand the role of the INILESt factor in our asset pricing equation, consider a simple return-generating process: (5) which can be re-written as: (6) The term βiINILESIt captures the time variation in the liquidity beta and makes the beta effectively βiINIL during the regular (calm) seasons and βiINILES +βiINIL during the earnings seasons months that exhibit announcement clustering. We denote βiINILES as the conditional liquidity beta. We follow the standard Fama and MacBeth (1973) two-pass procedure to estimate the factor premia in equation (5) with additional factors added – including B/M, Size, and Momentum. We use the entire sample in the first-pass beta estimation since the rolling beta approach is redundant because the liquidity beta is effectively time-varying as in equation (5).
3.6. Characteristics of liquidity portfolios
To test our second hypothesis that is the liquidity risk premium varies across seasons, we form 25 test portfolios by sorting NYSE, AMEX, and NASDAQ stocks on the book-to-market ratio (B/M) and the price-impact proxy (ILLIQ) using NYSE breakpoints. The practice of forming portfolios of assets is very common and is used to get sufficient variation in the variables of interest (see Fama and French (1993,1996) who use Size and Book-to-Market). Following this method we try to produce sufficient dispersion in liquidity betas while at the same time representing as diverse a cross section as possible. Thus we replace the sorting by size with that by ILLIQ.6 The portfolios are formed at the end of each year from 1964 through 2006, and the value-weighted monthly portfolio returns are calculated for the subsequent years from January 1965 through December 2006. 7 As usual, stocks are admitted to portfolios if they have the end-of-the-year prices between $5 and $1000 and more than 100 daily-return observations during the year to avoid “penny stocks” and stocks with infrequent trading. To get some idea about the test assets used in this section, we first look at the characteristics of the ILLIQ-sorted decile portfolios in Panel A of Table 5 where Rank 1 corresponds to the lowest ILLIQ (most liquid) and rank 10 the highest (most illiquid). To compute the portfolio characteristics presented in Table 5, we compute pre-ranking ILLIQ for each stock at the end of each year. The annual ILLIQ is then used for portfolio formation. All the returns and characteristics in the table are time-series averages of post-ranking monthly portfolio returns and characteristics. These monthly portfolio returns and characteristics are calculated each month as value-weighted cross-sectional averages of member stocks‟ returns and
In the robustness section below we run our tests with the returns on the conventional B/M by Size portfolios with essentially the same results. 7 As in previous sections, we use compounded daily returns to calculate the monthly returns for shifted months.
characteristics except for size (which is a simple cross-sectional average) and the number of stocks. These procedures are similar to those used in Watanabe and Watanabe (2008) and size and B/M characteristics are computed after Fama and French (1993) Consistent with the results reported in previous studies on the illiquidity premium (Amihud (2002), Acharya and Pederson (2005)), the average raw return generally increases with ILLIQ. Other characteristics exhibit expected near-monotonic relations with the ILLIQ ranking. Thus, more illiquid stocks tend to have more volatile ILLIQ, lower price, smaller market cap (Size) and greater B/M. These results suggest that it is important to control for the size and value factors as well as the illiquidity-level characteristic in our asset pricing test. We note that the most illiquid portfolio contains eight times as many stocks as other portfolios indicating that NASDAQ stocks are generally less liquid than NYSE stocks. Panel B of Table 5 reports selected summary statistics for the 25 portfolios formed at the intersection of B/M and ILLIQ quintiles (rank 1 has the lowest value of each characteristic). In Panel B(i), we observe that the average raw returns generally increase with both B/M and ILLIQ. Moreover, the illiquidity effect is stronger for value stocks (in the bottom rows) and the B/M effect is strong except for the most liquid stocks (the left-most column). Panel B(ii) confirms that we get dispersion in post-ranking illiquidity levels as measured by ILLIQ. The dispersion is slightly wider for value than growth stocks. Achieved variation shown in this table justifies our portfolio approach and we are ready to look into the main results of this section.
3.7. Main results
Using the 25 portfolios sorted on B/M and ILLIQ, we estimate factor premia each month by using the cross-sectional regression in equation (5) with additional factors. Table 6 reports the time-series means of the risk premia and their p-values. Column 1 shows the simplest model including only MKT, INIL, and INILES (the conditional liquidity factor). The INIL premium is negative and significant with INILES positive but not significant. A significantly positive constant and a significantly negative MKT premium, however, suggest omitted factors and that the model is grossly misspecified. Column 2 introduces INILES, which corresponds to the model in equation (5). While the INIL premium remains significant, INILES carries an insignificant premium. However, since both the constant and the MKT premium are still significant (MKT with the wrong sign), there are still significant factors missing. Column 3 adds the size (SMB) factor. The factor enters insignificantly with a very small coefficient but actually adds significance to the INILES factor leaving the significance of the intercept and the MKT essentially unchanged. The next column (4) adds B/M factor (HML) to the model used for column 3. At this point the intercept‟s coefficient drops (but still remains significant at the conventional levels) and the MKT factors become insignificant. INILES however survives the inclusion of this factor at better than 1% level of significance. When, finally we include the last commonly used factor (column 5), the momentum, (UMD), the contribution of the INILES remains very high end highly significant. The overall conclusion is that the announcement clustering of earnings seasons introduce undiversifiable liquidity risk to investors and they require additional risk premia for holding securities that are most sensitive to the liquidity shocks during these periods.
3.8. Robustness checks 3.8.1 Sample without NASDAQ
Many studies, including Acharya and Pederson (2005) or Pastor and Stambaugh (2003), avoid using NASDAQ firms arguing that this market‟s structure may affect the accuracy of reported volumes. Researchers that do use NASDAQ firms overcome that problem by using a “rule of thumb” when they simply half the reported NASDAQ volume (see Atkins and Dyl (1997) for the discussions on the validity of the rule). We argue that the inclusion of NASDAQ firms and the positive and significant results that we obtained with this sample show that our findings are applicable to the whole universe of stocks. However, to alleviate possible concerns that the results could be driven by the peculiar characteristics of the NASDAQ marketplace, we run our asset pricing tests on the restricted sample that includes only NYSE and AMEX securities. Table 7 shows the time series means of the risk premia and their p-values computed using exactly the same procedure as above but on the restricted sample with all NASDAQ firms dropped. As we can see the magnitude of the coefficients decreases but the significance and all the signs are the same. The results indicate that the findings are not driven just by the inclusion of the smaller NASDAQ stocks and that the liquidity effects of earnings seasons are “felt” across the whole universe of stocks (though a little bit stronger for smaller stocks which is completely natural since the latter are much less liquid). 3.8.2 Alternative assets
Since we sort the stocks into 25 portfolios by B/M and illiquidity, our sorting could bias the results towards our hypothesis of changing liquidity risk premium. To see if the results still 28
stand if we consider the traditional sorting, we run our asset pricing tests on 25 portfolios sorted by B/M and Size (we follow Fama and French (1993, 1996) in constructing the portfolios). Table 8 shows the average monthly risk premia for two samples. The full sample includes the stocks from all three exchanges NYSE, AMEX, and NASDAQ, while the restricted sample contains only stocks from NYSE and AMEX. As we can see the results are supportive of our hypothesis. However, the model with the full sample appears to be better specified since both the constant and the MKT factor are not significant at the 10% level. Even though the conditional liquidity factor (INILES) is significant “only” at the 6% level in both samples, the results are still much stronger than the ones obtained for the similar assets in other studies on liquidity. For example, Acharya and Pederson (2005) conclude that “With B/M-by-size portfolios, the model performs poorly.” Similarly, Watanabe and Watanabe (2008) obtain results significant only at the 8% level with the same test assets. Also, as in the previous subsection, the values of the premia even though smaller than for the original sorting are still of the same magnitude (again the INILES values are several times higher for the full sample). To summarize, the robustness checks conducted in this section supports the important role that the earnings seasons play in affecting the changes in liquidity risk premiums. The next section estimates the economic effect of this variability. 3.9. Economic significance
It is also important to estimate the economic impact of the changes in the conditional liquidity risk due to earnings seasons. In this section, we follow Acharaya and Pederson‟s (2005) approach by computing the annual return premium required to hold the same portfolio in two different time periods (calm vs. earnings seasons). This is computed as the product of the 29
additional risk premium and the difference in liquidity risk (betas) across the two states. Specifically, the effect of the earnings season on the smallest decile is -λ (βINILES –βINIL) x 12 months x 100%, that is -1.297x (-0.00407-(-0.00376)) x12x100% = 0.48% per year. The effect of the earnings seasons on the largest decile is -1.297 x (-0.00259-(-0.00104)) x 12 x 100% = 2.41% per year. To summarize, the additional risk premium required by the portfolio return‟s sensitivity to earnings seasons varies between 0.5% and 2.5% per year. The estimates appear reasonable. If we compare them with those obtained by Acharya and Pederson (2005) – between 0.25% and 2% per year – our results suggest that most of that premium comes from the sensitivity of returns to the illiquidity shocks produced by the earnings announcement clustering.
4. Summary and concluding remarks Just in the last 10 years scholarly journals have published several hundred papers with the keywords “earnings announcement.”8 Clearly, this is one of the most dynamic and important areas in accounting and financial research. The importance of earnings announcements for the firm‟s value has long been recognized and several well know anomalies associated with the announcement periods, including the post-earnings-announcement-drift and the announcements premium, have been documented. Despite the flood of research on this important topic, none of these studies look at the impact of earnings announcement clustering on the overall market. This is especially surprising since all earnings announcements (for every public corporation in the US) are concentrated within a relatively short window of 40 to 45 days after the end of each calendar quarter. The basic intuition tells us that if the individual earnings are so important, then
We use ABI Inform database to search for the keyword “earnings announcement” after 01/01/1998 and find 240 scholarly articles.
their aggregate concentrated impact might be important too. The intuition could be (and often is) wrong and that is why a thorough study of this phenomenon is necessary. First, we review the literature to establish some stylized facts related to the individual earnings announcements. Most researchers agree that just before the earnings release the trading volume dramatically declines but surges right after the announcement is made. The bid-ask spread widens and the depth for each price level declines precipitously. The common explanation for the observed patterns is the variation in information environment. As the earnings announcement date approaches the possibilities for informed trading increases driving uninformed traders out of the markets and forcing the market makers to protect themselves against such trading by widening spreads and reducing depths. Second, we investigate the impact of earnings seasons on three economically-important variables that could affect overall market liquidity. Specifically, we establish that controlling for January effect, the equal-weighted CRSP index returns are significantly lower during earnings seasons. The fact that the value-weighted index returns are not significantly different from the returns during the calm periods indicates that this time period impacts mostly small firms and which in turn is consistent with the special informational role of the earnings seasons. 9 The aggregate trading volume during earnings seasons exhibits the same pattern as the trading volume of individual firms during their quarterly announcements. Specifically, the volume significantly decreases during the first couple of weeks of the earnings season, then surges closer to the middle of the earnings season, and then drops to the normal level. This is consistent with the view that noise (liquidity) traders exit the market at the beginning of the 9
For larger firms, the quarterly and annual reports are not as important since they frequently release information in between and usually have good business press and analyst coverage.
season due to the heightened probability of trading with an informed trader, only to start trading actively after the information release when the uncertainty is mostly resolved. The third variable that we deal with in the first part of the paper is volatility. We determine that aggregate volatility, as measured by the CBOE VIX index, drops sharply exactly during the week that precedes the start of the earnings seasons. Since the VIX measures the expected volatility over the next 30 days, this drop in VIX values confirms that traders are very much aware of the special information status of earnings seasons. After we establish the economic significance of the earnings seasons for unconditional returns, trading volumes, and volatility, we examine the effect of these time periods on asset prices controlling for known factors. A straightforward way to investigate this connection is to directly examine the liquidity effects of earnings seasons. If we can establish that during the earnings seasons markets experience liquidity shocks, then using the burgeoning literature on the commonality of liquidity we can study the asset pricing connection within an established framework (Acharya and Pederson (2005), and Pastor and Stambaugh (2003)). During the first step, we select a liquidity measure (Amihud‟s illiquidity) and test whether the earnings seasons are characterized by different (from the regular seasons) liquidity betas. We in fact find that liquidity betas are significantly lower (more negative) during the earnings seasons. This finding agrees with others who also find negative and significant liquidity betas (Acharya and Pederson (2005), Amihud (2002), and Amihud et al (2005)). The last part of the paper investigates whether there is an additional liquidity risk premium that is required because of the sensitivity of stock‟s return to the liquidity shocks during the earnings seasons. We construct a conditional liquidity factor and employ the most commonly 32
used asset pricing testing procedure, the Fama-Macbeth regressions, to test whether this conditional factor is priced. By adding the commonly used factors one by one, we explore their effect on the magnitude and the significance of the conditional liquidity risk premium. We find that after including HML (book-to-market), UMD (momentum), INIL (unconditional liquidity factor), SMB, and MKT (CRSP value-weighted index), our INILES (conditional liquidity factor) is still significantly priced. To summarize, this paper is the first to demonstrate the importance and economic significance of earnings announcement clustering during earnings seasons. There are several possible avenues of further research. Among them are questions on whether this identified liquidity premium is due to real or information frictions (Stoll, 2000). Also interesting is the question of how this premia varies across different earnings seasons since we know that earnings seasons themselves are not all created equal. Several recent papers (e.g., Ng, 2006)), argue that liquidity effects are related to the magnitude and direction of earnings surprises and not to the announcements per se. Perhaps, to even better capture the liquidity effects we should differentiate the earnings seasons by the ratio of bad to good surprises. This direction is also consistent with the general trends in the accounting literature that moves towards greater differentiation of the effects related to earnings seasons to explain the well-known anomalies. Still other directions call for investigation of the effects in other than equity markets such as derivatives (options and credit-default swaps), where the information‟s impacts on the prices is amplified. No matter what the direction of future studies is going to be, the recognition of the importance of earnings seasons on asset prices will definitely improve our understanding of financial markets.
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Fig. 1. The number of firms reporting each week covered by COMPUSTAT Quarterly database (19712006). The fraction of firms covered by the database increases from less than 50% in the 1970s to almost 100% in 2000s.
Fig. 2. The average number of firms reporting each week for the period from 1971 to 2006. This striking pattern stays relatively constant for every year in the period covered .
Fig. 3. The average (over 1962-2006) aggregate weekly share turnover in percent (a thick line) imposed over the average number of firms that report during that week (bar). First we calculate the share turnover for each firm for each week. Then we calculate the aggregate share turnover for each week by simpleaveraging the individual share turnovers and multiply the resulting time series by the 24-week average (a scale factor to remove the overall increasing trend). Finally, we average the aggregate weekly share turnovers over 45 year period (1962-2006). To aid the visual comparison we divided the number of firms reporting by 200 and added a polynomial (5th degree) trend line for the turnover series.
Table 1: Distribution of fiscal year-ends for firms in the COMPUSTAT Quarterly Database (1971-2006) This table shows the average distribution of Fiscal-Year-Ends (FYE) by months. Within 75 to 90 days after the firm‟s year-end it has to file the annual report. The highlighted months (in bold) are the months in which the Earnings seasons begin. The majority of the FYE falls on December. The table does not show the distribution of quarterly earnings (they are shown in the Figure 2 above). Month (FYE) January February March April May June July August September October November December
Number of firms 47250 24002 81881 30651 30106 119772 30336 31418 94989 45570 25798 782019
Percent of firms 3.52 1.79 6.09 2.28 2.24 8.91 2.26 2.34 7.07 3.39 1.92 58.19
Cumulative number 47250 71252 153133 183784 213890 333662 363998 395416 490405 535975 561773 1343792
Cumulative percent 3.52 5.3 11.4 13.68 15.92 24.83 27.09 29.43 36.49 39.89 41.81 100
Table 2: Seasonality in returns This table shows the results of simple OLS regression with dummy variables for the earnings
seasons. The depended variable is excess returns on CRSP Equal- or Value- weighted CRSP indices and the independent variable is one of the three proxies. We use three different proxies for the earnings seasons: the first two weeks after the end of each quarter, the one full month, and the first 45 days after the end of each calendar quarter. Panel A presents the results for the full sample (1962-2006) and panel B with the first two weeks of January removed. The star (*) denotes the values significant at 5% or better. First two weeks coefficient p-value
One month coefficient
45 days coefficient
A. Full Sample Equal-Weighted Returns Value-Weighted Returns
B. Without 2 first weeks of the year Equal-Weighted Returns Value-Weighted Returns
Table 3: Seasonality in Aggregate Trading Volume This table shows the seasonality in aggregate trading volume as measured by the Share Turnover. First we calculate the share turnover for each firm for each week. Then we calculate the aggregate share turnover for each week by simple-averaging the individual share turnovers. Finally, we average the aggregate weekly share turnovers over 45 year period (1962-2006). To get the estimates in each row we run simple OLS with respective dummies for the earnings seasons. The dependent variable is the aggregate scaled average weekly share turnover and the independent variable is one of the four dummies: first two weeks, middle two weeks, one full months, and full 45 day season. The star (*) denotes the values significant at 5% or better. A. Full Sample coefficient
B. Without the January Effect coefficient p-value
Dummy for: The first two weeks
The middle two weeks
45 day season
Table 4: Liquidity betas This table shows the results of testing whether the liquidity betas are different (lower) during the earnings seasons. , where the dependent variable is the excess return on the size-sorted decile portfolios (NYSE
breakpoints). INIL is the unconditional liquidity factor- the innovations in market-wide liquidity constructed after Amihud (2002) and Acharya and Pederson (2005). ES is the dummy for earnings season months (shifted by two weeks) (January, April, July, and October). INILES is the conditional liquidity factor. It equals INIL during the earnings seasons and zero otherwise. The star (*) denotes the values significant at 5% or better.
intercept INIL ES INILES
Smallest Decile Coefficient p-value * 0.01243 0.00 * -0.00376 0.00 0.00113 0.85 * -0.00407 0.02
Largest Decile Coefficient p-value * 0.00504 0.02 * -0.00104 0.09 0.00417 0.28 * -0.00259 0.03
All Coefficient p-value 0.00137 0.15 * -0.00291 0.00 0.00121 0.46 * -0.00321 0.00
Table 5: Portfolio characteristics This table shows the characteristics of test portfolios. Panel A shows the characteristics of 10 ILLIQ-sorted portfolios with average characteristics. We compute pre-ranking ILLIQ for each stock at the end of each year which is then used for portfolio formation. All the returns and characteristics in the table are time-series averages of post-ranking monthly portfolio returns and characteristics. These excess monthly portfolio returns and characteristics are calculated each month as value-weighted cross-sectional averages of member stocks‟ returns and characteristics except for size (which is a simple cross-sectional average) and the number of stocks. The Size and B/M characteristics are computed after Fama and French (1993). All months in the study are shifted by two weeks forward. Panel B shows the characteristics of 25 test portfolios sorted on B/M and ILLIQ (with rank 1 being the lowest in each category. Panel B(i) shows returns for each portfolio, and Panel B(ii) shows ILLIQ values. Panel A. ILLIQ-sorted portfolio characteristics Decile
10 Panel B.
Table 6: Estimated risk premia for the full sample This table shows estimated monthly percentage premia for different models. The predictor variable is the returns on 25 test asset sorted on B/M and ILLIQ. MKT is the excess returns on CRSP value-weighted index, INIL is the liquidity factor (innovations in Amihud (2002) illiquidity measure). INILES is the conditional liquidity factor equal INIL during the earnings season months and zero otherwise. UMD is the momentum factor. HML and SMB are B/M and size factors obtained from K. French‟s website and the monthly returns are recalculated for our shifted (by two weeks forward) months. The estimation period covers 42 years (504 months of data) of data from 01/01/1965 to 12/31/2006. The star (*) denotes the values significant at 5% or better.
Const. MKT INIL INILES SMB HML UMD
1 Premia p-val. * 0.019 0.00 * -0.013 0.00 * -1.707 0.01
2 3 4 5 Premia p-val. Premia p-val. Premia p-val. Premia p-val. * * * * 0.013 0.00 0.025 0.00 0.009 0.02 0.008 0.03 * * -0.015 0.01 -0.02 0.00 -0.004 0.37 -0.004 0.41 * * -0.912 2.092 0.02 0.04 1.3279 0.17 1.3204 0.15 * * * 1.387 1.300 1.297 0.0229 0.34 0.00 0.00 0.00 0.0001 0.96 0.0011 0.44 0.0011 0.43 * * 0.005 0.00 0.005 0.00 -0.002 0.69
Table 7: Estimated risk premia for the restricted sample (only NYSE and AMEX stocks) This table shows estimated monthly risk premia for different models. The predictor variable is the returns on 25 test asset sorted on B/M and ILLIQ. MKT is the excess returns on CRSP valueweighted index, INIL is the liquidity factor (innovations in Amihud (2002) illiquidity measure). INILES is the conditional liquidity factor equal INIL during the earnings season months and zero otherwise. UMD is the momentum factor. HML and SMB are B/M and size factors obtained from K. French‟s website and the monthly returns are recalculated for our shifted (by two weeks forward) months. The estimation period covers 42 years (504 months of data) of data from 01/01/1965 to 12/31/2006. The star (*) denotes the values significant at 5% or better.
Const. MKT INIL INILES SMB HML UMD
1 Premia p-val. * 0.0167 0.00 * -0.012 0.00 * -0.101 0.02
2 3 4 5 Premia p-val. Premia p-val. Premia p-val. Premia p-val. * * * * 0.017 0.02 0.01 0.00 0.00 0.01 0.009 0.04 * * -0.013 -0.02 0.00 0.00 -0.005 0.29 -0.003 0.46 * * -0.097 0.187 0.02 -0.024 0.75 0.03 0.1650 0.07 * * * * 0.143 0.168 0.151 0.143 0.01 0.00 0.01 0.02 0.0010 0.52 0.0022 0.14 0.0023 0.13 * * 0.006 0.00 0.006 0.00 0.0015 0.80
Table 8: Estimated risk premia for the alternative assets (B/M by Size) This table shows estimated monthly risk premia for two samples. The full sample includes stocks from NYSE, AMEX, and NASDAQ. The restricted sample includes only NYSE and AMEX stocks. The predictor variable is the returns on 25 test asset sorted on B/M and SIZE. MKT is the excess returns on CRSP value-weighted index, INIL is the liquidity factor (innovations in Amihud (2002) illiquidity measure). INILES is the conditional liquidity factor equal INIL during the earnings season months and zero otherwise. UMD is the momentum factor. HML and SMB are B/M and size factors obtained from K. French‟s website and the monthly returns are recalculated for our shifted (by two weeks forward) months. The estimation period covers 42 years (504 months of data) of data from 01/01/1965 to 12/31/2006. One star (*) denotes the values significant at 5% or better and two stars (**) denote the values significant at 10% or better. Full sample coefficient p-value Const. MKT INIL INILES SMB HML UMD
0.0067 -0.0017 0.3214 ** 0.8948 0.0026
Restricted sample coefficient p-value 0.0164
-0.0107 0.0682 ** 0.1147
0.70 0.74 0.06
0.00 0.05 0.37 0.06 0.01 0.01 0.14